How many solutions does the system of equations below have? y = 7x + 6 y = 7x + 7/2 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Slope Analysis: System of equations: y = 7x + 6 y = 7x + 7/2 Are the slopes same or different? Slope of first equation: 7 Slope of second equation: 7 Slopes of the equations are the same.Y-Intercept Comparison: System of equations: y = 7x + 6 y = 7x + 7/2 Are the y-intercepts same or different? y-intercept of first equation: 6 y-intercept of second equation: 7/2 (which is 3.5) y-intercepts of the equations are different.Number of Solutions: System of equations: y = 7x + 6 y = 7x + 7/2 Determine the number of solutions to the system of equations. The system of equations has the same slope but different y-intercepts. The system of equations has no solution because they are parallel lines.

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How many solutions does the system of equations below have? $\newline$ $y = 7x + 6$ $\newline$ $y = 7x + \frac{7}{2}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Algebra 1

Find the number of solutions to a system of equations

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Q. How many solutions does the system of equations below have?

\newline

y = 7x + 6

\newline

y = 7x + \frac{7}{2}

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Choices:

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(A)no solution

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(B)one solution

\newline

(C)infinitely many solutions

Slope Analysis: System of equations: $\newline$ $y = 7x + 6$ $\newline$ $y = 7x + \frac{7}{2}$ $\newline$ Are the slopes same or different? $\newline$ Slope of first equation: $7$ $\newline$ Slope of second equation: $7$ $\newline$ Slopes of the equations are the same.
Y-Intercept Comparison: System of equations: $\newline$ $y = 7x + 6$ $\newline$ $y = 7x + \frac{7}{2}$ $\newline$ Are the y-intercepts same or different? $\newline$ y-intercept of first equation: $6$ $\newline$ y-intercept of second equation: $\frac{7}{2}$ (which is $3.5$ ) $\newline$ y-intercepts of the equations are different.
Number of Solutions: System of equations: $\newline$ $y = 7x + 6$ $\newline$ $y = 7x + \frac{7}{2}$ $\newline$ Determine the number of solutions to the system of equations. $\newline$ The system of equations has the same slope but different y-intercepts. $\newline$ The system of equations has no solution because they are parallel lines.